PREDICTION–BASED TESTS FOR MISSPECIFICATION IN NONLINEAR SIMULTANEOUS SYSTEMS

Abstract

This chapter discusses the prediction-based tests for misspecification in nonlinear simultaneous systems. Asymptotic bias in the stochastic predictor, because of misspecification, can be expressed linearly in terms of chosen functions of a list of variables, including the exogenous variables in the system. Analysis of model misspecification is a critical issue in econometric theory. Within the context of a nonlinear simultaneous model, where predictive performance can be important, for example, for forecasting or policy analysis, an alternative approach can be to design specification error tests with power against misspecification, which adversely affects the prediction performance. The prediction-based tests provide consistent tests of misspecification against which the usual estimation-based tests have no power. Application of the regression test to the linear model reduces to a comparison of the restricted and unrestricted reduced form coefficient estimates and is a test for the validity of all the over-identifying restrictions in the model.